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Impedance Z and Admittance Y



You are expected to learn how to :
Compute the current I expected flowing in any RLC circuit.
Then compute the current I1 and I2
Then compute the expected total power consumption and then compute the power consumption of impedance load 1 Z1 and the power consumption of impedance load 2 Z2


YT = 1 / ZT Explain why 1 / 4.472 ZT is not equal to Z=11.18 as shown by graphical complex number addition? Answer: The two impedances are not in series, so the complex number addition will not work because in parallel you compute the total impedance using the formula 1/Z1 + 1/Z2. To make the calculation easy admittance concept was introduced.

FORMULA RECALL : Y is the Admittance and Z is the Impedance.

Important to remember inductive load is represented by + J (positive reactance) and capacitive load - J (negative reactance) . This knowledge is very important because of the complex number conjugate when you are doing complex number division. This calculator embedded that reactance rule + j L (use positive for inductive load) and - J C (use negative for capacitive load) that affects the complex number conjugate. So be careful not to put negative sign in capacitive input box shown below. It's already accounted for.

Y 1 = 1 / Z1 = + J = °

Memory recall knowledge of complex number division using conjugate.

Y 2 = 1 / Z2 = + J = °

Y = Y 1 + Y 2 Total Admittance , YT = 1 / ZT
Y 1 + Y 2 = + J = °

I = I 1 + I 2 = E * Y = Total Current
* ° = °

I 1 = E * Y 1
* =

I 2 = E * Y 2
* =

I 1 = + J

I 2 = + J

I = + J =

P = E * I * Cos (-10.3049) = * * = Watts

P 1 = E * I1 * Cos (-36.87) = * * = Watts

P 2 = E * I2 * Cos (53.1303) = * * = Watts

Initial, I 1 = magnitude. See above for angle in °
Initial, I 2 = magnitude. See above for angle in °
Initial, I = magnitude. See above for angle in °

INITIAL DATA

R4 = 4 XL = 3
R6 = 6 XC = 8
V = 100

No need to add the negative sign for capacitive reactance because it is already embedded in the logical computation.



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